The deadline for the homework is the end of our class session next week (Dec 20, 2023) A TV company produces Smart TVs. The company wants to plan production and workforce levels for the next 6 months. The table below shows the number of workdays and Smart TV demand (in thousands) for each month. Note that if the demand is exceeded, the leftovers can be carried to the next month. If the demand is not satisfied, the items are backordered. The annual inventory holding cost per Smart TV is $120. If the company cannot satisfy a demand on time, a backorder cost of $30 is incurred. Additionally, past data shows that 25 workers can produce 60 thousand Smart TVs in 20 days. The company currently has 35 workers and 3000 Smart TVs in stock. The company incurs a hiring cost of $800 and firing cost of $1200 per worker. The company cannot hire or fire more than 10% of its workforce in any month (i.e., if there are 30 workers at the end of a month, they can hire or fire a maximum of 3 people starting next month). The payroll is $60 per worker per day. Suppose that the company cannot change the number of workers they have for the first 3 months. The company also aims to have at least 25 workers and 10 Smart TVs in stock at the end of the 6 month planning horizon. Write a Linear Programming (LP) model that identifies the workforce and production plan, aiming to minimize the total cost